IRR Calculator

The internal rate of return — the discount rate at which a project’s net present value is exactly zero.

Last updated September 1, 2026

Your details

Cash flows

The first figure is period 0 — enter the initial outlay as a negative number.

Compare against

Your cost of capital, for a verdict. Optional.

Result

Internal rate of return: 21.86%
Sum of cash flows: $600.00
NPV at the IRR: $0.00
Against a 10.00% hurdle: Accept

Solving for the rate that zeroes the NPV…

0 = Σ CFₜ ÷ (1 + IRR)ᵗ

5 flows, from $-1,000.00 at t=0

No closed form exists — the rate is found by narrowing a bracket

NPV at 21.8623% = $0.00

IRR = 21.86%

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Formula — written step by step

1,000 out, then 400 back four times…

0 = Σ CFₜ ÷ (1 + IRR)ᵗ

Try 20%: NPV = +35.49

Try 25%: NPV = −55.36

The root lies between them

Narrow the bracket until NPV ≈ 0

IRR = 21.86%

IRR is the discount rate at which the project exactly breaks even. There is no formula that solves for it directly, so it is found by testing rates and closing in — which is what the calculator does, to nine decimal places.

A worked example

Comparing two projects of different sizes

Project A: −1,000 then 600, 600
Project B: −10,000 then 5,500, 5,500
Cost of capital: 8%

A: IRR = 13.07%, NPV at 8% = 69.96
B: IRR = 6.60%, NPV at 8% = −192.04
A has the higher rate of return
A also has the positive NPV

Choose A — it clears the 8% hurdle and B does not

Here both measures agree. They often do not: a small project can have a spectacular IRR while creating little value, and a large one a modest IRR while creating a great deal. When ranking mutually exclusive projects, NPV is the measure to follow.

How to use this calculator

Enter the cash flows in order, beginning with period 0. The initial investment must be negative and at least one later flow positive.
Enter your cost of capital in the comparison box for an accept-or-reject verdict.
Read the IRR as the project’s own break-even rate — the return it generates on the capital tied up in it.
Check the "NPV at the IRR" row: it should be zero. That is the calculator proving its own answer rather than asking you to trust it.

What the internal rate of return means

The IRR is the discount rate at which a project’s net present value is exactly zero — the return the project earns on the money tied up in it, expressed as an annual percentage. If it exceeds your cost of capital, the project is creating value; if it falls short, it is destroying it.

Its appeal is that it needs no assumption to compute. NPV requires you to nominate a discount rate before you get an answer; IRR produces a rate from the cash flows alone, which is why it travels so well in conversation.

Why there is no formula

Setting NPV to zero and solving for the rate produces a polynomial of degree n, and polynomials above the fourth degree have no general algebraic solution. So IRR is found numerically: guess a rate, see whether the NPV is positive or negative, and narrow the range.

This calculator uses bisection rather than the faster Newton’s method, deliberately. Newton can diverge on flat or awkwardly shaped cash-flow series, returning nonsense without warning. Bisection cannot: given a sign change to work within, it always converges. The trade is a few more iterations for an answer that is never wrong.

The reinvestment assumption, and where IRR misleads

IRR implicitly assumes every interim cash flow is reinvested at the IRR itself. For a project returning 40%, that means assuming each year’s proceeds also earn 40% — rarely true, and it flatters high-IRR projects systematically.

There is a second trap. When cash flows change sign more than once — an outlay, returns, then a large closure or restoration cost — the polynomial can have several real roots, and several rates can legitimately zero the NPV. This tool reports the first root above −100% and shows the NPV alongside it. If your flows change sign repeatedly, treat the IRR as indicative and decide on NPV.

Formula & methodology

IRR is the rate r solving 0 = Σ CFₜ ÷ (1 + r)ᵗ. No closed form exists; it is found numerically by bisection to a tolerance of 1e−9.

What this calculator assumes

Assumes interim cash flows are reinvested at the IRR itself — often optimistic. Where that is doubtful, NPV at an explicit cost of capital is the sounder test.
A series whose sign changes more than once can have several mathematically valid IRRs. This tool reports the first root found in the bracket above −100% and should be read alongside NPV.
Where the flows never cross zero — all positive or all negative — no IRR exists, and the calculator says so rather than returning a misleading number.

Sources

Brealey, Myers & Allen, Principles of Corporate Finance, 13th edition, McGraw-Hill, 2019 — the internal rate of return rule and its pitfalls.

IRR against NPV

	IRR	NPV
Expressed as	A percentage	An amount of money
Needs a discount rate?	No	Yes
Reinvestment assumption	At the IRR itself	At the discount rate
Multiple valid answers?	Possible when signs change repeatedly	Never
Ranking rival projects	Unreliable — ignores scale	Reliable

IRR is easier to communicate and NPV is easier to trust. Where the two disagree about which project to choose, follow NPV.

Frequently asked questions

Why does it say there is no IRR?

Because the cash flows never cross zero — they are all positive or all negative. With no sign change there is no rate at which the series balances, so no IRR exists. Returning a nearby number would be worse than saying so.

Can a project have more than one IRR?

Yes. Each change of sign in the cash flows can introduce another root. A project with an outlay, returns, then a large decommissioning cost may have two mathematically valid IRRs, neither more correct than the other.

Is a higher IRR always better?

No. IRR ignores scale entirely: a 60% return on 1,000 creates far less value than a 15% return on a million. For ranking projects you could choose between, use NPV.

What is MIRR?

Modified IRR fixes the reinvestment assumption by discounting outflows at your finance rate and compounding inflows at a realistic reinvestment rate. It usually gives a lower, more believable figure than IRR.